Whether Hotaka forgives her mother or not, I wouldn't judge it. She could forgive her but never forget and shut her off of her life, or be like how Wahei and their dad did. In the end, it all depends whether she thinks that mother could still be fitted into her life. But the latter seems to be someone's wishful thinking as she casted her two little sisters as well. At the very least, I imagine she'd treat her coldly, and do just up until what the law and her morals needs her to do as a daughter.
If I remember correctly, the father did abandon them, but that was with the knowledge they had their mother and then soon, when the mother left them, he told them about their brother. Though that is still a shitty move, and god forbids me to pull out the keys to our truck. He at least had the concern to have them stay in a warm house, and even said he'll try to make time to meet them. Still a shitty damn father. (Do your job properly. ╬)
I think forgiveness can also mean to set the problem out of a one's way so, they could walk forward. They won't forget it but, they won't let that person weigh them down anymore, in heart and thoughts. Completely cutting off the road that connects them with that person. That's how I perceive forgiveness in such a situation at least.